In Exalted 3e, each of the major types of exalted that I have the books for has at least a chance of passing on supernatural traits to their children, except apparently the Solars.
The children of the Dragon-blooded have a chance of being Dragon-blooded themselves. The children of Lunars are often Moon-Touched with a variety of possible powers including possible limited transformation (Lunars, p. 18). The children of Sidereals are Star-Blessed and might inherit a small amount fate-related magic (Sidereals Compiled Draft, p. 12).
But if the Solars have anything equivalent I have not found it. Was this a deliberate omission and there is nothing inherently special about the children of Solars, or did I perhaps miss something?